Question 24 (2 points) Which represents the solution to the inequality below in interval notation? -3vert n-5vert -11lt -38 a (-4,14) b (-14,4) (-infty ,-14)cup (4,infty ) d (-infty ,-4)cup (14,infty )

To solve the inequality $-3\vert n-5\vert -11\lt -38$, we first isolate the absolute value expression:<br /><br />$-3\vert n-5\vert -11\lt -38$<br /><br />Add 11 to both sides:<br /><br />$-3\vert n-5\vert \lt -27$<br /><br />Divide both sides by -3 (and reverse the inequality sign):<br /><br />$\vert n-5\vert \gt 9$<br /><br />This inequality means that the distance between $n$ and 5 is greater than 9. We can split this into two separate inequalities:<br /><br />$n-5 \gt 9$ or $n-5 \lt -9$<br /><br />Solving these inequalities gives:<br /><br />$n \gt 14$ or $n \lt -4$<br /><br />In interval notation, this is represented as:<br /><br />$(-\infty,-4)\cup (14,\infty )$<br /><br />So, the correct answer is:<br /><br />d) $(-\infty,-4)\cup (14,\infty )$